A Toeplitz-like Operator with Rational Symbol Having Poles on the Unit Circle II: The Spectrum

Abstract

This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum, is given, as well as a description of the essential spectrum. In this case, the essential spectrum need not be connected in $\mathbb{C}$. Various examples illustrate the results.